One embodiment of the present invention relates to a force sensor array having magnetostrictive multilayer sensors, and to a method for determining a force acting on the carrier of a force sensor array. Such force sensor arrays are used, for example, for determining a pressure which deforms the diaphragm of a pressure sensor.
Magnetostrictive magnetoresistive layer systems make use of the effect according to which their electrical resistance changes under the influence of an external force. In particular the GMR (gigantic magnetoresistive) effect and the TMR (tunnel magnetoresistive) effect are known in this context.
Such a magnetoresistive layer system includes a layer sequence with two or more magnetic layers which each have one magnetization direction. When the layer sequence is deformed, for example under the influence of an external tensile force or compressive force, by virtue of the magnetostrictive properties of the layers, the orientation of the magnetization directions of the individual magnetic layers with respect to one another changes, which, due to the magnetoresistive effect, brings about a change in the electrical resistance of the layer sequence.
Such a layer sequence includes at least one hard magnetic first layer which serves as a reference layer, and one soft magnetic second magnetic layer which serves as a measuring layer. Each of these magnetic layers has magnetization with one magnetization direction. While the magnetization direction in the first magnetic layer is fixed with respect to the layer sequence by suitable measures, the magnetization direction of the second magnetic layer can change under the influence of an external force acting on the layer sequence, while the magnetization direction of the first magnetic layer retains its original position owing to the fact that it is fixed. As a result a change occurs in the angle enclosed by the two magnetization directions, and this thus entails a change in the electrical resistance of the layer sequence.
This effect can be used to determine the force acting on a layer sequence by determining the electrical resistance of the layer sequence.
FIG. 1 shows by way of example a typical multilayer system according to the prior art. The multilayer system includes a layer sequence 1 along with a fixing layer 3, a fixed magnetic reference layer 11, a nonmagnetic separating layer 22 and a magnetic measuring layer 12.
FIG. 2 illustrates an enlarged vertical section through a portion of the layer sequence according to FIG. 1.
The fixing layer 3 is composed, for example, of a natural antiferromagnet (IrMn, PtMn, NiO) and it gives the desired stability to the reference layer (12) which is coupled to it by direct exchange coupling (for example in external fields, “exchange bias field”).
The reference layer 11 can alternatively also be embodied as what is referred to an artificial antiferromagnet. This is a layer system composed of two magnetic layers which are coupled antiferromagnetically to one another and have a nonmagnetic coupling layer between them.
The reference layer 11 is coupled antiferromagnetically to the fixing layer 3.
Given suitably selected dimensioning of the coupling strength between the fixing layer 3 and the reference layer 11, the magnetization direction M1 of the reference layer 11 is also fixed with respect to the layer system 1 and remains itself unchanged when there is a tensile force or compressive force acting on the layer system 1.
The measuring layer 12 is spaced apart from the reference layer 11 by means of a separating layer 22. The measuring layer 12 has a magnetization direction M2 which extends, for example, perpendicularly with respect to the magnetization direction M1 of the reference layer 11.
FIG. 3a shows a plan view of the layer sequence 1 which is in the quiescent state, according to FIGS. 1 and 2. Quiescent state here refers to the state in which there is no external tensile force or compressive force or external magnetic field acting on the layer sequence 1.
In this view, the perpendicular arrangement of the magnetization directions M1 and M2 of the reference layer 11 and of the measuring layer 12 with respect to one another can be seen.
However, this array for measuring an external force acting on the layer system has a serious disadvantage which will be explained below with reference to FIGS. 3b and 3c. 
It is a precondition that the reference layer 11 has a negligible magnetostriction, which can be achieved technically by, for example, suitably selecting the composition of the alloy. Accordingly, the alloy does not react at all, or reacts only slightly, to external mechanical stresses. The stability in the present case is also additionally favored by the exchange coupling to the fixing layer 3.
If an external force F, for example a tensile force, acts parallel to the magnetization direction M1 of the reference layer 11 on the layer sequence 1, this force effect causes the preferred position of the magnetization direction M2 of the measuring layer 12 to change.
In the unstressed state said position was perpendicular with respect to the magnetization M1 of the reference layer 11. The preferred position of the magnetization M2 of the measuring layer is achieved by a marked degree of shape anisotropy of the layer system 1 in the xy plane.
The effect of an external force on the magnetization direction M2 of the measuring layer 12 is determined here by the direction of the force and by the sign of the magnetostriction constant λ12 of the measuring layer 12.
If the magnetostriction constant λ12 is greater than zero when the tensile force F is acting, the magnetization direction M2 of the measuring layer 12 exhibits a tendency to increasingly orient itself parallel to the axis C of the acting tensile force F as the magnitude of the tensile force increases (case 1).
If, in contrast to the illustration, the force F were a compressive force acting on the layer system 1, the magnetization direction M2 of the measuring layer 12 would have the tendency to orientate itself increasingly perpendicularly with respect to the axis C of the acting compressive force as the magnitude of the compressive force increases (case 2).
If the magnetostriction constant λ12 of the measuring layer 12 is smaller than zero with the tensile force F is acting, its magnetization direction M2 would orientate itself increasingly perpendicularly with respect to the axis C of the acting tensile force F as the magnitude of the tensile force increases (case 3).
Furthermore, when there is a negative magnetostriction constant λ12 of the measuring layer 12 and a compressive force acting on the layer system 1, the magnetization direction M2 of the measuring layer 12 would orient itself increasingly parallel to the axis C of the acting compressive force as the magnitude of the compressive force increases (case 4).
In cases 1 and 4 it would, however, be the same in terms of energy whether the magnetization direction M2 changes by, as shown in FIG. 3b, an angle Δφ1 in, or as shown in FIG. 3c, an angle Δφ2 against the direction of the acting force F owing to the tensile force F acting on the layer system 1 starting from its quiescent position illustrated in FIG. 3a. The decisive factor is that the magnetization direction M2 preferably rotates in the direction of the axis of tensile stress in both cases shown in FIGS. 3b and 3c. 
In the case in FIG. 3b, the magnetization directions M1 and M2 of the reference layer 11 or measuring layer 12 enclose an angle φ1 which is smaller than the angle φ2, between the magnetization directions M1, M2 of the reference layer 11 and of the measuring layer 12 in the case in FIG. 3c. 
As the magnitude of the tensile force F increases, an antiparallel orientation of the magnetization directions M1, M2 would be brought about in the borderline case of infinitely high acting force in FIG. 3b, and a parallel orientation of the magnetization directions M1, M2 would be brought about in the borderline case of infinitely high acting force in FIG. 3c. 
Since the electrical resistance of the layer sequence 1 depends on the cosine of the angle φ1 in FIG. 3b or φ2 in FIG. 3c, which is enclosed by the magnetization directions M1, M2 of the reference layer 11 and measuring layer 12, the layer sequence has a different electrical resistance in the case in FIG. 3b than in the case in FIG. 3c although the same external tensile force F acts on the layer sequence 1 in both cases.
Furthermore, under the conditions described in cases 2 and 3, the preferred orientation of the magnetization direction of the measuring layer 12 would point in a direction perpendicular with respect to the acting force F (or its axis C). However, since the initial position (FIG. 3a) is distinguished by the perpendicular orientation of M1 and M2, there would be no change in the preferred orientations, and thus also no change in resistance.